The present disclosure relates to indicator assemblies having multiple modular indicator elements. Examples of such assemblies include assemblies sometimes known as “tower lights,” “stack lights” or “tower stack lights.” Such assemblies find wide range of applications, from safety, automation and workflow management in industrial settings to status indication in office settings. In a typical assembly of this kind, multiple indicator modules, such as LED light modules, which are typically cylindrical in shape, are connected together in series along a longitudinal axis. The module at one end of a series is connectable to a base having multiple electrodes, each connected to a wire or connector pin for conducting electrical signal (i.e., power) from a signal source, such as a controller, to the respective electrode. Each module may have multiple conductors running from one end of the module to the other, typically near or inside the cylindrical housing wall of the module. When the modules are connected together, the conductors form multiple conductive paths through the assembly such that each of the conductors in each module is connected to a corresponding electrode in the base to receive an electrical signal. Each module also has one or more indicator circuits, such as LED elements, often with associated electronic components for various purposes, such as intermittent signaling and surge protection. The indicator is typically connected to one of the conductors. The angular position (rotational about the longitudinal axis) between each pair of adjacent modules is typically fixed, for example by bayonet-type mounts. Thus, the order of the modules in the series typically determines which electrode in the base corresponds to the indicator circuit in each module. Such an arrangement imposes certain constraints and complications on the design and deployment of such indicator assemblies and associated components such as controllers and cables.